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# If x is an integer, what is the value of x? (3)

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If x is an integer, what is the value of x? (3) [#permalink]  17 Nov 2008, 14:41
If √x is an integer, what is the value of √x?
(3) 11<x<17
(4) 2<√x<5
________________________________________________________________
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: value integer [#permalink]  17 Nov 2008, 17:08
I agree with A.

With (1), there's only one possible number in that range of 12 to 16 that x could be for it to be a perfect square (x has to be 16).

With (2), square root of x could be either 3 or 4 so there's no unique solution.
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Re: value integer [#permalink]  17 Nov 2008, 18:54
I feel it should be E.

1 statement is insufficient since x has to be 16 and root of 16 can be +4 or -4

2 is insufficient since it could be 3 or 4
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Re: value integer [#permalink]  17 Nov 2008, 22:07
since √x is under a radical, its supposed to be positive...although im not too sure...any comments on this?
jitendra wrote:
I feel it should be E.

1 statement is insufficient since x has to be 16 and root of 16 can be +4 or -4

2 is insufficient since it could be 3 or 4
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Re: value integer [#permalink]  17 Nov 2008, 22:38
haichao wrote:
If √x is an integer, what is the value of √x?

(3) 11<x<17
(4) 2<√x<5

Agree that its not A but it is also not E.

From (1) since sqrt(x) is an integer, x has to be 16 but sqrt(x) could be -4 or 4. so insuff...
From (2) sqrt(x) could be 3 or 4. still not suff.

But from 1 and 2, sqrt(x) is 4.

so C.
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Re: value integer [#permalink]  17 Nov 2008, 23:00
GMAT TIGER wrote:
haichao wrote:
If √x is an integer, what is the value of √x?

(3) 11<x<17
(4) 2<√x<5

Agree that its not A but it is also not E.

From (1) since sqrt(x) is an integer, x has to be 16 but sqrt(x) could be -4 or 4. so insuff...
From (2) sqrt(x) could be 3 or 4. still not suff.

But from 1 and 2, sqrt(x) is 4.

so C.

I think sqrt(16) results in a positive number - so sqrt(16) = 4, not -4.
However, when x^2 = 16, then you can have 2 values of x: 4 and -4.
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Re: value integer [#permalink]  18 Nov 2008, 00:22
nganle08 wrote:
I think sqrt(16) results in a positive number - so sqrt(16) = 4, not -4.
However, when x^2 = 16, then you can have 2 values of x: 4 and -4.

Yep, GMAT considers positive square root only.
A should be the correct answer.
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Re: value integer [#permalink]  18 Nov 2008, 00:27
Agree with Tiger

(1) is insufficient due to the fact that 16 has two roots, +- 4. I would be surprised if GMAT would only consider the positive root, as I think it is incomplete to say that sqrt(16)=4 rather than +-4. When you take a square root, you are asking: which number, when squared, gives the desired result? For 16 there are clearly two answers and neither one alone is complete.

(2) is also insufficient by itself since sqrt(x) could be 3 or 4.

Together, (1) and (2) show that the answer is sqrt(x)=4.
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Re: value integer [#permalink]  18 Nov 2008, 09:25
phdizzle wrote:
Agree with Tiger

(1) is insufficient due to the fact that 16 has two roots, +- 4. I would be surprised if GMAT would only consider the positive root, as I think it is incomplete to say that sqrt(16)=4 rather than +-4. When you take a square root, you are asking: which number, when squared, gives the desired result? For 16 there are clearly two answers and neither one alone is complete.

(2) is also insufficient by itself since sqrt(x) could be 3 or 4.

Together, (1) and (2) show that the answer is sqrt(x)=4.

You can disagree with it but GMAT says that square root will only take positive value. So sqrt(16) = 4 only.
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Re: value integer [#permalink]  18 Nov 2008, 12:01
alpha_plus_gamma wrote:
nganle08 wrote:
I think sqrt(16) results in a positive number - so sqrt(16) = 4, not -4.
However, when x^2 = 16, then you can have 2 values of x: 4 and -4.

Yep, GMAT considers positive square root only.
A should be the correct answer.

Can someone substantiate this one. I mean is it written in the OG somewhr??

For me the answer has to be C
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Re: value integer [#permalink]  18 Nov 2008, 13:46
hibloom wrote:
alpha_plus_gamma wrote:
nganle08 wrote:
I think sqrt(16) results in a positive number - so sqrt(16) = 4, not -4.
However, when x^2 = 16, then you can have 2 values of x: 4 and -4.

Yep, GMAT considers positive square root only.
A should be the correct answer.

Can someone substantiate this one. I mean is it written in the OG somewhr??

For me the answer has to be C

I do not bring my OG with me now, but in Manhattan GMAT prep "Number Properities", it says "Unlike even exponents, which yeilld both a positive and a negative solution, square roots have only one solution. Ex: sqrt(4) = 2. While it is true that (-2)(-2) = 4, the GMAT follows the standard convention that a radical (root) sign denotes only the non-negative root of a number. Thus, 2 is the only solution for sqrt(4)."
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Re: value integer [#permalink]  18 Nov 2008, 15:01
going with A on this one..you have only positive sqrt(x)
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Re: value integer [#permalink]  18 Nov 2008, 15:04
haichao wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5

A

1. Since √x is an integer, x = 16
So, √16 = 4 - Suff

2. InSuff
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Re: value integer [#permalink]  19 Nov 2008, 16:39
Wow, thanks nganle. As much as that surprises me it's good to know! Although I will undoubtedly forget come test time thanks to too many years of brain-programming...
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Re: value integer [#permalink]  20 Nov 2008, 01:33
Quote:

I do not bring my OG with me now, but in Manhattan GMAT prep "Number Properities", it says "Unlike even exponents, which yeilld both a positive and a negative solution, square roots have only one solution. Ex: sqrt(4) = 2. While it is true that (-2)(-2) = 4, the GMAT follows the standard convention that a radical (root) sign denotes only the non-negative root of a number. Thus, 2 is the only solution for sqrt(4)."

with this explanation, I will straightly go to A as my answer
Re: value integer   [#permalink] 20 Nov 2008, 01:33
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# If x is an integer, what is the value of x? (3)

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